Model Reference Gaussian Process Regression: Data-Driven Output Feedback Controller

Data-driven controls using Gaussian process regression have recently gained much attention. In such approaches, system identification by Gaussian process regression is mainly followed by model-based controller designs. However, the outcomes of Gaussian process regression are often too complicated to apply conventional control designs, which makes the numerical design such as model predictive control employed in many cases. To overcome the restriction, our idea is to perform Gaussian process regression to the inverse of the plant with the same input/output data for the conventional regression. With the inverse, one can design a model reference controller without resorting to numerical control methods. This paper considers single-input single-output (SISO) discrete-time nonlinear systems of minimum phase with relative degree one. It is highlighted that the model reference Gaussian process regression (MR-GPR) controller is designed directly from precollected input/output data without identification of the system itself.